What was discussed

He said this was part of consolidating the "1992 consensus" - the agreement under which both sides recognise the principle of "one China" but define it in their own ways.

Similar remarks were made by Mr Xi, who said upholding the consensus would help "the great rejuvenation of the Chinese nation".

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Media captionChina-Taiwan relations in 60 seconds

Why are they meeting now?

It is not entirely clear why the meeting has happened at this time, as neither side has properly said.

Mr Ma has built his presidency on closer links with China, so there is a good reason for him to meet Mr Xi, says the BBC World Service's Asia editor, Michael Bristow.

There is also a presidential election in Taiwan in January. Mr Ma might think the meeting will give a boost to his party's candidate, who is trailing in the polls, our correspondent says.

China also has something to gain, and that also concerns Taiwan's election. Mr Xi's decision to talk reminds Taiwanese voters that China is far friendlier to a government of Mr Ma's nationalist party than one formed by the opposition, which leans towards independence for Taiwan.

It is a calculated gamble for Mr Xi, as China's attempts to influence Taiwanese voters have previously backfired, our correspondent adds.

Taiwan-China key dates

1949: Chiang Kai-shek's Kuomintang (KMT) nationalists form their own government in Taiwan after Mao Zedong's communists take power in Beijing

1971: Taiwan loses its seat at the UN to China

1979: The US establishes diplomatic relations with China while at the same time committing itself to defending Taiwan

1993: First direct talks between the two sides take place in Singapore

2005: Beijing brings in a law that makes secession by Taiwan illegal, at the risk of military action

2008: High-level talks between the two sides resume after Ma Ying-jeou is elected president